is a field if and only if is irreducible if and only if has no zeros in .

2) Find the degree of and a basis for E = Q

Let then since is an irreducible polynomial which has as a root it means is a basis. This means are linearly independent. Thus, are linearly independent and so they spam a vector space of dimension three.

[tex]
Let then since is an irreducible polynomial which has as a root it means is a basis. This means are linearly independent.
Thus, are linearly independent and so they spam a vector space of dimension three.